Transcription, the way Chinese words are spelled with the Western alphabet, has varied over time - and still does. The Chinese pictogram is an image of the word and its meaning, but it says nothing about pronunciation. The Western alphabet, though, is all about that. So, when Chinese words are written with our ABC, we need to decide how they are pronounced.
But that's not as easy as it seems. There are lots of different dialects in China, also there's an uncertainty about how words were pronounced previously in Chinese history. So, several systems of transcription have been created, in different periods of our own history.
The most established one for ancient Chinese texts is called the Wade-Giles transcription, developed in the 19th century. Its spelling for this word is ch'i, often simplified to chi. In the mid-20th century, the Chinese government presented their own system of transcription, called Pinyin, in which the word is spelled qi. This was accepted as the international standard in 1982.
But the old spelling ch'i or chi remains in wide use, especially on the Internet. Old habits die hard. Also, Wade-Giles remains the most popular transcription for the Chinese classics, where it is deemed by many experts to fit the best.
The Pinyin reform goes slowly, and seems to be almost retreating because of the Internet, where the old spelling is usually preferred. But things are happening. Google regards them - correctly - as different spellings of the same word, so search results for one spelling also bring results of the other.
I made a comparison of the search terms "chi energy" and "qi energy" on Google (December 2015). The former got 132 million hits, the latter 69 million. But in both searches, the spellings are mixed - due to Google knowing it's the same thing.
Google Trends, the service showing the popularity of search terms over time, also reveals that it's still very much the older spelling that people use in their searches. See the diagram below (from December 4, 2015), where "chi energy" is the blue line and "qi energy" the red. Even today, the former spelling is searched distinctly more often than the latter. But they are closing in on one another.
The spelling "ch'i", though, is getting obsolete also on the Internet. A search for "ch'i energy" returned only 0.4 million results (not much on Google) and the search engine suggested: "Did you mean chi energy?"
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